John Terrell

WHAT CAN NETWORK ANALYSIS ACCOMPLISH beyond data mining, mapping, and fancy (or plain) visualization? Not an easy question to answer. The published literature on networks is enormous. I am going to focus now, therefore, only on social network analysis with the understanding that later I will have things to say, as well, about other applications.

If all you have is a hammer

Consider the popular expression often attributed (wrongly, it seems) to Mark Twain: “if all you have is a hammer, everything looks like a nail.” Having recently surveyed the last ten years of research papers published in the journal Social Networks, I think it is possible to say a few things in general about the state of this research pursuit. While there are numerous exceptions, of course, many doing social network analysis seem so committed to the established structuralist view of networks that this saying might just as well be rephrased as “if all you have is a network, everything looks like a structure.” Since what I mean by saying this is probably far from clear, here’s the issue I have with this narrowly focused sociological take on network analysis.

There are only so many ways a given number of things (call them N) can be connected together, mathematically speaking. For example, the maximum number of simple ties among N=10 things is N(N-1)/2, i.e., 45. Therefore, even if we must know for some excellent reason how N=10 things are linked (that is, “structured”) in ways equal to or less than this maximum number of ties, surely this cannot be all we need to know to understand why these ten things are structurally connected with one another in one way or another.

Yet what I have taken away from reviewing the past ten years of research papers in Social Networks is that the focus of much of the work being reported is often more about methodology—the “hammer,” so to speak—than about what to build with it worth the investment of time, money, and effort.

A limited tool kit

Here’s another way of saying what I just said. While going through articles in this journal I was repeatedly surprised that network analysis seems to be used only rarely to model and test explanatory research hypotheses. Instead, even when real-world data are included as part of the exercise, what is often invoked are a small number of social network’s own proprietary analytical concepts labeled as “parameters” and “social processes” used in ways which are not only descriptive but often also seemingly explanatory (e.g., Fitzhugh and Butts 2018). Typical examples are these: centrality, density, transitivity, clustering, reachability, and so forth (Hanneman and Riddle 2005). I won’t try to explain here what these are, but include links that describe them in some detail.

I find it is hard to know what to make of these so-called parameters and processes. For instance, here is what one well-known online handbook tells us about the sociological concept of power: “All sociologists would agree that power is a fundamental property of social structures. There is much less agreement about what power is, and how we can describe and analyze its causes and consequences.” Following this candid but confusing observation, we are then told:

Network thinking has contributed a number of important insights about social power. Perhaps most importantly, the network approach emphasizes that power is inherently relational. An individual does not have power in the abstract, they have power because they can dominate others—ego’s power is alter’s dependence.

What I want to underscore about this assertion is that apparently such an observation is not being offered to us as a research hypothesis suitable for testing against data. Instead, we are evidently being asked to accept this portrayal of power, whatever you take it to be, as a statement of truth.

Why do network analysis?

The passages quoted above come from a standard and extremely helpful introduction to social network methods by Robert Hanneman and Mark Riddle published back in 2005. This guide for the perplexed is still freely available on the Internet today. These authors are careful to tell us what they see as the three main reasons for using the methods they describe. Here they are, rewritten to abbreviate them:

The matrices and graphs at the heart of network analysis are compact and systematic ways to manage information and manipulate data efficiently so we can detect structural patterns that otherwise can be tedious to document and hard to see;

since these methods are quantitative and mathematical, we are able to use computers to analyze networks data, even massive amounts of it; and

these rules and methodological conventions can help us do more than communicate effectively; they can also help us discover things in our data we might not even think to look for using only words to describe and summarize the relationships reflected in the information we have.

You may disagree, but I think these three strengths are basically those I have previously labeled as mining, mapping, and visualization, although I haven’t yet mentioned using computers.

In any case, I am certainly not alone in thinking there is more to social network analysis than just these three strengths. As these authors themselves say in the afterword that concludes their handbook:

The basic methods of studying patterns of social relations that have been developed in the field of social network analysis provide ways of rigorously approaching many classic problems in the social sciences. The application of existing methods to a wider range of social science problems, and the development of new methods to address additional issues in the social sciences are “cutting edge” in most social science disciplines.

Unfortunately, they say nothing at all about what these problems and additional issues may be. Their closing words are simply these:

we have not touched on very much of the substance of the field of social networks—only the methodologies. Methods are only tools. The goal here is using the tools as ways of developing understanding of structures of social relations. The most obvious next step is to read further on how network analysis has informed the research in your specific field. And, now that you are more familiar with the methods, you may see the problems and possibilities of your substantive field in new ways.

Integrative networks

Despite these inconclusive words at the end of this influential handbook, social network analysis has never been solely about mathematical methods and formal procedures. In 2012, for example, an issue of Social Networks was entirely devoted to exploring the common ground between social network research and geographic spatial analysis even though it was acknowledged that “the formal integration of social network and spatial analytic strategies remains relatively underdeveloped in the literature” (Adams et al. 2012: 1).

Although there have been advances since then such as the use of adaptive network modeling in restoration ecology (Raimundo et al. 2018) and in understanding how violent crime effects inter-neighborhood community patterns in Chicago (Graif et al. 2017), this goal still seems a long way off.

Does this matter? Perhaps not if all that you want to do is map and visualize the relationships among N things, people, or places to offer plausible interpretations of the observed structural arrangements, but is this the most that network analysis can hope to achieve (Doreian and Conti 2012)?

Over forty years ago (Terrell 1977), I suggested that similarities and differences among local human populations reflect the workings of an integrated complex of variables and relationships that can be idealized as a geographic system (Figure 1).

Figure 1. “The concept of geographic systems can be described using an elementary model to depict how local populations and the habitats they occupy may all be seen as interrelated within a comprehensive network of interactions. The concept itself may be defined as follows: a geographic system is the interactive configuration among the size, distribution and interaction structure of a set of local populations and the elements and interaction structure of the area of their occurrence, analysed as a complex of intercommunicating variables within which a change in any one variable or relationship is likely to effect changes, of a greater or lesser degree, in all the others. It probably is not necessary to add that such a complex of variables and relationships is unlikely to respond only to single causes, although changes in some dimensions may be more influential on the system as a whole than changes in others” (Terrell 1977: 65).

Back then I knew that from this integrative perspective it wouldn’t do to reply on categorical units labeled for convenience as “populations,” “habitats,” “geographic regions,” and the like. At this same time, therefore, I began to explore using network approaches inspired by work in locational geography (Terrell 1976). As shocking as it may seem to network sociologists, I knew absolutely nothing at that time about the work of Harrison White, one of the founders of the modern sociological networks tradition, even though I had been an undergraduate and later a graduate student at Harvard. The distance between Anthropology and Sociology there in Cambridge, Massachusetts, back then was not geographic but social and cultural.

I was also inspired by ecology and biogeography as practiced then. But here, too, I saw one had to be careful not to borrow from other disciplines without being watchful. As I wrote in 1977:

the geographic system concept resembles that of an ecosystem and encompasses the trophic or food relations between man and his environment which are specifically explored by human ecologists. The concept, nevertheless, is intended to be more inclusive than that of an ecosystem, in order to avoid the a priori assumption that an analysis of the interactions within and among human populations can be reduced to a study of the trophic, biochemical and species structures of their environment and the functioning of those structures. (Terrell 1977: 65).

While I won’t try to detail the reasons, I was also dissatisfied with the idea that the Earth can be subdivided into geographic regions, and with the convention back then that networks are systems (nowadays I would be more vocal about saying that systems are networks, but not all networks are systems).

A geographic system . . . is a set of biological and ecological elements, their structural relationships, and their functional operation. . . . [W]hile geographic regions have spatial boundaries by definition, geographic systems do not. All the communities living within a region may be usefully called a regional population, yet it is conceivable and even likely that a given region, defined spatially, may house two or more fairly distinct “system populations” which interact little if at all among each other.

Even thus qualified, I felt more needed to be said, and followed these observations with words of caution. “The world in all its complexity is not, after all, a mosaic of discrete parts or ‘regions'” (Terrell 1977: 66).

Dynamic networks

Given the hindsight of 40+ years, I would now visualize what I was trying to say differently (Figure 2). Had it also been a low-cost publishing option back then, I undoubtedly would have opted to use color, not that doing so makes much difference except possibly in the visual appeal of the model:

Figure 2

What either version of this conceptual model hopefully conveys is that while one could be committed professionally to researching just a single relational dimension in this complex of relationships—as it seems most doing social network analysis today prefer to do—if you want to learn not just how social relations are structured but also why, then it would be naive to assume what you are observing can be explained solely by social properties and processes.

I have argued previously that something can be called a “relationship” if what you have in mind is repetitive, situational, contingent, and consequential. Additionally, I have also noted that two other dimensions need to be added when the relationships are social: intentional and purposeful.

But this is not all. Without any explanation I added earlier that another dimension needs to be included: adaptation (Figure 3).

Figure 3

I will have much to say about adaptive networks in future posts in this series. At this point, since this one is longer than I like already, let me just give you a simple example of what I have in mind.

From a sociological perspective, what happens in a hospital operating room is unquestionably an example of a small functioning social network. Ignoring the role of the patient on the table for a moment, everyone in the room has a role to play and is related to everyone else in clearly defined ways (much more clearly defined, by the way, than would be normal outside the medical and legal environment of the operating theater).

It seems reasonable that if one wanted to, many of the standard parameters and social processes favored in sociological network analysis can be employed to mine, map, and visualize what is going on over the supine (or prone) figure lying on the operating table. But if one then stopped paying attention to the work being done, what would be the point of even just being there to witness the operation?

What would soon become painfully apparent if you stayed around longer is that as the surgical team proceeds with the operation at hand not merely because they want to (what they are doing, in other words, is obviously intentional), but also because they hope to achieve a particular outcome (the operation is, after all, purposeful), who does what, why, when, how, and even whether evolves dynamically to meet the changing contingencies of what they come across once the patient is anesthetized, opened up, and the work begins in earnest.

What’s next

What is happening in this hypothetical operating theater is a simple example of what I want to talk about in future posts in this series when I am exploring with you not just how but also why it is good to study networks of human engagement between things, places, and people as dynamic, adaptive, evolving strategies—not just structures—for survival.